A Simple Image Compression :
JPEG
Overall Process :
• The image is broken into 8x8 blocks of pixels
• Working from Left to Right and Top to Bottom, Discrete Cosine
Transform(DCT) is applied to each of the 8x8 blocks.
• Each Block is compressed through Quantization
• The array of compressed blocks that constitute the image is stored in a
drastically reduced amount of space.
• The image is reconstructed by the use if Inverse Discrete Cosine
Transform(IDCT).
DCT Computation
The DCT Coefficient D(i,j) for the (i,j) pixel
is computed as follows:
DCT Computation
For a standard (8x8) block as used in jpeg, N=8 and
(x,y) range from 0 to 7. Hence, the DCT computation
has reduced to:
Matrix Representation of the
DCT Equation
Let Tij be computed as :
Matrix form of T
ij
For an (8x8) block, it results in the matrix:
DCT Computation on an (8x8)
Block
DCT Computation
DCT Computation
DCT Computation
Quantization
Quantization
Quantization Levels
Quantization Levels
Quantization
Quantization
Zeros represent less important higher
frequencies that can be discarded.
Coding
Decompression
Inverse DCT and Decompression
Comparison
Finally ….
Further Levels